Linear Equation Calculator
Solve linear equations of the form ax + b = c. Find the value of x step by step. Works for one-step, two-step, and multi-step linear equations with fractions and decimals.
∑ Algebra📐 ax + b = c → x = (c - b) / a🔢 Math
Coefficient a
Constant b
Right side c
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Linear Equation Calculator | — | ax + b = c → x = (c - b) / a | x value |
Step-by-Step Examples
Example 1
Simple
3x + 5 = 20
- 3x = 20 - 5 = 15
- x = 15/3 = 5
- Check: 3(5)+5=20 ✓
✓ x = 5
Example 2
Negative
−2x + 8 = 14
- −2x = 14 − 8 = 6
- x = 6/(−2) = −3
- Check: −2(−3)+8=14 ✓
✓ x = −3
Example 3
Decimal
0.5x − 1.2 = 3.8
- 0.5x = 3.8+1.2 = 5.0
- x = 5.0/0.5 = 10
✓ x = 10
Real-World Applications
Education
Most common algebra problem type — taught in every middle and high school worldwide.
Finance
Solve for unknown in cost equations: 3x + 50 = 200.
Science
Rearrange physics formulas: v = u + at → solve for t.
Data Analysis
Linear interpolation and trend line calculations.
Common Mistakes to Avoid
⚠️
Dividing by negative flips inequality
For equations it is fine. But if you later use this in an inequality, dividing by negative a flips the sign.
⚠️
Coefficient of 0
If a = 0: either no solution (0x = 5) or infinite solutions (0x = 0). Check before dividing.
⚠️
Forgetting to distribute
3(x+2) = 9 → 3x + 6 = 9, not 3x + 2 = 9.
Frequently Asked Questions
What is a linear equation? ▾
An equation where the variable appears to the first power only (no x², no √x). Graph is always a straight line.
How do I solve multi-step equations? ▾
1) Distribute, 2) Combine like terms, 3) Move variable terms to one side, 4) Move constants to other side, 5) Divide by coefficient.
What if there is no solution? ▾
When both sides simplify to a false statement like 5 = 3, the equation has no solution. When both sides simplify to a true statement like 3 = 3, it has infinitely many solutions.
How do I check my answer? ▾
Substitute x back into the original equation. Both sides must be equal.
What is a literal equation? ▾
An equation solved for one variable in terms of others, like solving d = rt for t: t = d/r. Same process, just letters instead of numbers.
Related Math Calculators
Formula Explorer connections
Interpretation: This formula describes an algebraic relationship among variables, functions, equations, roots or sequences. Assumption: Respect the expression’s domain and excluded values. Check roots in the original equation because transformations can introduce extraneous solutions.